Typical research results on the nonlinear dynamics of beams subject to axially base excitation were established at the end of 1970s[1].Since then, great attention has been paid to the nonlinear dynamics of the beams over the past few decades due to both theoretic and practical demands.However, the excitation to the beams mainly focused on the deterministic one and the significance of random excitation has not been highlighted.Some scholars[2] experimentally investigated the planar response of a cantilever beam vertically excited by a shaker, however, the definite overhang or jumping phenomena in their experimental results were not well explained and described using the deterministic theory.